Probing Sol-Gel Matrices and Dynamics of Star PEG Hydrogels Near Overlap Concentration

Although numerous studies have been conducted to describe the gelation of multi-arm star polymers, reports on the relationship among rheological quantities, overlap concentration (c*), and microstructures have still remained insufficient. Here, we examine the sol-gel dynamics of hydrogels formed by 4-arm poly(ethylene glycol) (PEG) near c* based on dynamic scaling theory. We investigated the evolution of viscoelastic modulus (storage modulus G' and loss modulus G '') with reduced gelation time (tau) and the normalized extent of crosslinking (epsilon), and a divergent dependence was observed near c*. A general expression of the Hill equation was employed to evaluate the complex modulus spectra and critical relaxation exponent (Delta) at the gel point (i.e., G' similar to G '' similar to omega(Delta)), providing a way to access such a critical exponent, regardless of how fast the gelation occurs. Besides, the dynamic scaling exponent with e shows high sensitivity to the pre-gel clusters and post-gel networks. Moreover, two-dimensional time-frequency viscoelastic mapping indicates that the hydrogel formed at c* shows higher homogeneity than those away from c*, and inhomogeneity of the local cluster density would contribute to the large-scale fluctuation in rheological quantities during gelation.